Residence Times Flashcards
Define ‘residence time’.
The actual time the fluid resides within the rector.
How do you calculate residence time?
t = V/u(t) u(t) = volumetric flow rate.
For a batch reactor, how can residence be calculated generally?
residence time = reaction time
Define ‘space time’.
The residence time when volumetric flow rate is constant throughout.
How do you calculate space velocity?
Sv = u(t)/V
-> inverse of space time.
How are residence times used to diagnose reactor problems?
An inert tracer is injected into the reactor inlet and the outlet concentration is continuously monitored.
What does a short residence time depict about a reactor?
By-passing -> reactants are not seeing the full volume of the reactor eg. short-circuiting & channeling
What does a longer residence time depict about a reactor?
Calculation error -> incorrect volume or volumetric flow eg. inlet volume not considered.
Poor mixing -> stagnant regions & short-circuiting.
Derive the formula for the time taken for a reaction to occur in a batch reactor.
For a liquid phase reaction, derive the residence time in a batch reactor.
n=reaction order
For a liquid-phase reaction with constant volume, derive the residence time in a batch reactor.
n=reaction order
t = 1/kNA^(n-1) x V^(n-1) x dxA/(1-x)^n
t = V^(n-1)/kNA^(n-1) x dxA/(1-x)^n
t = 1/kCA0^(n-1) x dxA/(1-x)^n
What is the equation for a first order, constant volume, gas phase reaction in a batch reactor?
t = -1/k ln(1-xA)
For a gas-phase reaction with constant pressure, derive the residence time for a batch reactor.
t = 1/kNA^(n-1) x V^(n-1) x dxA/(1-x)^n
NT = NT0 + ((vB+vC-vA)/vA) NA0 xA
NT/NT0 = 1 + eA xA
Ideal gas; V/V0 = NT/NT0 = 1 + eA xA
-> V = V0(1+eA xA)
t = 1/kCA0^(n-1) x (1+eA xA)^(n-1)/(1-xA)^n x dxA
For a liquid-phase reaction, derive the residence volume occupied in a PFR.
rA = kCA = knA/u(t) = k nA0^n (1-xA)^n/u(t)^n
u(t) = u(t0) (1+eAxA)
V = u(t0)/knA0^(n-1) x (1+eAxA)/(1-xA)^n dxA
For a constant volumetric flowrate, liquid-phase reaction, what is the residence volume occupied?
V = u(t0)/knA0^(n-1) x 1/(1-xA)^n dxA
What is the equation for the residence volume in a first order, liquid phase reaction in a PFR?
V = u(t)/k ln(1/(1-xA))
What is the equation for conversion of A in a first order, gas phase reaction in a PFR?
xA = 1 - e^(-kt)
Derive the equation for the volume of a CSTR from reaction rate.
rA = (nA0-nA)/V V = (nA0 xA)/rA
Derive the equation for the residence volume in a CSTR.
V = (nA0 xA)/rA
rA = kCA^n = k (nA/u(t))^n
u(t) = u(t0) (1+eAxA)
V = (nA0/k) x (1/CA0^n) x ((1+eAxA)^n/(1-xA)^n) x xA
For a first order reaction, define an equation for the mean residence time in a CSTR.
t = V/u(t) = 1/k x xA/(1-xA)
For a first order reaction, define an equation for the conversion of A in a CSTR.
xA = kt/(1+kt)
Why is the residence time defined as the mean residence time in a CSTR?
Not all molecules in a CSTR have the same residence time but instead are a distribution.
What does a shorter mean residence time depict in a CSTR?
At any one time, molecules will have been in the reactor for a range of residence times so this results in reduced conversion. eg. poor mixing.
In a CSTR, the longer a molecule spends in the reactor, the ___ conversion takes place.
More
In a batch/PFR reactor, the longer a molecule spends in the reactor, the ____ conversion takes place.
Same.
The composition (rate) changes with ___ in a batch reactor, ____ in a PFR and ____ in a CSTR.
Time,
Volume (length),
Nothing.
A CSTR operates at exit conditions so lower concentration results in ___ conversion, ___ reaction rate and ___ residence time to achieve the ___ conversion.
A CSTR operates at exit conditions so lower concentration results in higher conversion, lower reaction rate and longer residence time to achieve the same conversion.
Which is more common, constant pressure or constant volume batch reactors?
Constant volume
Why is space velocity used in PFRs rather than residence time?
Because it uses initial volumetric flow rate.
In an ideal batch/PFR reactor, molecules have ____ residence times.
Equal.
For a gas-phase reaction with constant volume, derive the residence time in a batch reactor.
n=reaction order
For a gas-phase reaction, derive the residence volume occupied in a PFR.
What will happen to the mean residence time in a CSTR if teperature increases?
P u(t) = nRT
As T increases, u(t) increases so;
t = V/u(t)
mean residence time will decrease.
For the following reaction A -> 2B with iner species C, when nA0=nC0=0.5, what is the nA/nT ratio?
nA/nT = (1-xA)/(2+xA)
Derive the equation for the reaction rate of A in terms of residence time and concentration for a CSTR.
rA = (nA0-nA)/V rA = xA nA0/V rA = xA CA0/(V/u) rA = xA CA0/t rA = (CA0 - CA)/t
For a first order reaction, at time t, will a CSTR or PFR have a higher conversion?
PFR
